Gas leak emission quantification with a gas cloud imager

ABSTRACT

An instrument and method for analyzing a gas leak. The instrument can obtain a time series of spectra from a scene. The instrument can compare spectra from different times to determine a property of a gas cloud within the scene. The instrument can estimate the column density of the gas cloud at one or more locations within the scene. The instrument can estimate the total quantity of gas in the cloud. The instrument can estimate the amount of gas which has left the field of view of the instrument. The instrument can also estimate the amount of gas in the cloud which has dropped below the sensitivity limit of the instrument.

INCORPORATION BY REFERENCE TO ANY PRIORITY APPLICATIONS

Any and all applications for which a foreign or domestic priority claimis identified in the Application Data Sheet as filed with the presentapplication are hereby incorporated by reference under 37 CFR 1.57. Inparticular, this application claims priority to U.S. Provisional PatentApplications 62/021,636, filed Jul. 7, 2014, 62/021,907, filed Jul. 8,2014, and 62/083,131, filed Nov. 21, 2014, all of which are entitled“GAS LEAK EMISSION QUANTIFICATION WITH A GAS CLOUD IMAGER,” and all ofwhich are incorporated by reference herein in their entirety.

BACKGROUND

Field

This disclosure generally relates to systems and methods for gas clouddetection and gas leak emission quantification.

Description of the Related Art

There are a wide variety of systems that create, store, transfer,process, or otherwise involve gases. These include, but are not limitedto, industrial systems, such as oil and gas drilling rigs andrefineries. In such systems, there may be a risk of gas leaks. Suchgases may include hydrocarbons (e.g., methane), ammonia, hydrogensulfide, volatile organic compounds, and many, many others. Gas leakscan pose safety and/or environmental risks. They can also result infinancial loss. It would therefore be advantageous to develop systemsand methods for detecting gas leaks and quantifying gas leak emission.

SUMMARY

In some embodiments, an infrared (IR) imaging system for quantifying oneor more parameters of a gas leak having a gaseous emission rate isdisclosed, the imaging system comprising: an optical system including anoptical focal plane array (FPA) unit, the optical system havingcomponents defining at least two optical channels thereof, said at leasttwo optical channels being spatially and spectrally different from oneanother, each of the at least two optical channels positioned totransfer IR radiation incident on the optical system towards the opticalFPA unit; and a data-processing unit comprising one or more processors,said data-processing unit configured to acquire multispectral opticaldata from the IR radiation received at the optical FPA unit and outputgaseous emission rate data for a gaseous leak.

In some embodiments, an infrared (IR) imaging system for quantifying oneor more parameters of a gas cloud is disclosed, the imaging systemcomprising: an optical system including an optical focal plane array(FPA) unit, the optical system having components defining at least twooptical channels thereof, said at least two optical channels beingspatially and spectrally different from one another, each of the atleast two optical channels positioned to transfer IR radiation incidenton the optical system towards the optical FPA unit; and adata-processing unit comprising one or more processors, saiddata-processing unit configured to acquire spectral optical data fromthe IR radiation received at the optical FPA unit, wherein saiddata-processing unit is configured to determine absorption spectra dataat a given pixel of a given frame by comparing spectral data for saidpixel of said frame with spectral data from prior frames.

In some embodiments, a system for quantifying one or more parameters ofa gas leak is disclosed, the system comprising: a communicationsubsystem for receiving multi-spectral optical data produced by a cameraincluding an optical focal plane array (FPA) unit, the camera havingcomponents defining at least two optical channels thereof, said at leasttwo optical channels being spatially and spectrally different from oneanother, each of the at least two optical channels positioned totransfer IR radiation incident on the optical system towards the opticalFPA, said multi-spectral optical data derived from the IR radiationreceived at the optical FPA; and a data-processing unit comprising oneor more processors, said data-processing unit configured to acquire saidmultispectral spectral optical data from said communication subsystem,wherein said data-processing unit is configured to process saidmultispectral optical data and output gaseous emission rate data from agaseous leak.

In some embodiments, a system for quantifying one or more parameters ofa gas leak is disclosed, the system comprising: a communicationsubsystem for receiving processed data derived from multi-spectraloptical data produced by a camera including an optical focal plane array(FPA) unit, the camera having components defining at least two opticalchannels thereof, said at least two optical channels being spatially andspectrally different from one another, each of the at least two opticalchannels positioned to transfer IR radiation incident on the opticalsystem towards the optical FPA, said multi-spectral optical data derivedfrom the IR radiation received at the optical FPA; and a data-processingunit comprising one or more processors, said data-processing unitconfigured to acquire said processed data from said communicationsubsystem, wherein said data-processing unit is configured to furtherprocess said processed data and output gaseous emission rate data for agaseous leak.

In some embodiments, a system for quantifying one or more parameters ofa gas cloud is disclosed, the system comprising: a communicationsubsystem for receiving multi-spectral optical data produced by a cameraincluding an optical focal plane array (FPA) unit, the camera havingcomponents defining at least two optical channels thereof, said at leasttwo optical channels being spatially and spectrally different from oneanother, each of the at least two optical channels positioned totransfer IR radiation incident on the optical system towards the opticalFPA, said multi-spectral optical data derived from the IR radiationreceived at the optical FPA; and a data-processing unit comprising oneor more processors, said data-processing unit configured to acquire saidmulti-spectral optical data from said communication subsystem, whereinsaid data-processing unit is configured to determine absorption spectradata at a given pixel of a given frame from a comparison of spectraldata for said pixel of said frame with spectral data from prior frames.

In some embodiments, a system for quantifying one or more parameters ofa gas cloud is disclosed, the system comprising: a communicationsubsystem for receiving multi-spectral optical data produced by a cameraincluding an optical focal plane array (FPA) unit, the camera havingcomponents defining at least two optical channels thereof, said at leasttwo optical channels being spatially and spectrally different from oneanother, each of the at least two optical channels positioned totransfer IR radiation incident on the optical system towards the opticalFPA, said multi-spectral optical data derived from the IR radiationreceived at the optical FPA; and a data-processing unit comprising oneor more processors, said data-processing unit configured to acquire saidmulti-spectral optical data from said communication subsystem, whereinsaid data-processing unit is configured to compare spectral data forsaid pixel of said frame with spectral data from prior frames for thedetermination of absorption spectra data at a given pixel of a givenframe.

In some embodiments, a system for quantifying one or more parameters ofa gas cloud is disclosed, the system comprising: a communicationsubsystem for receiving optical data produced by a camera including anoptical focal plane array (FPA) unit, the camera having componentsdefining at least two optical channels thereof, said at least twooptical channels being spatially and spectrally different from oneanother, each of the at least two optical channels positioned totransfer IR radiation incident on the optical system towards the opticalFPA, said multi-spectral optical data derived from the IR radiationreceived at the optical FPA; and a data-processing unit comprising oneor more processors, said data-processing unit configured to acquire saidoptical data from said communication subsystem, wherein saiddata-processing unit is configured to consider noise as a criteria fordetermining whether to include data for the given pixel for a particularprior frame with data from other prior frames for comparing spectraldata for a pixel of a later frame with spectral data from prior framesfor the determination of absorption spectra data for the given pixel ofthe later frame.

In some embodiments, an infrared (IR) imaging system for quantifying oneor more parameters of a gas cloud is disclosed, the imaging systemcomprising: an optical system including an optical focal plane array(FPA) unit, the optical system having components defining at least twooptical channels thereof, said at least two optical channels beingspatially and spectrally different from one another, each of the atleast two optical channels positioned to transfer IR radiation incidenton the optical system towards the optical FPA unit; and adata-processing unit comprising one or more processors, saiddata-processing unit configured to acquire spectral optical data fromthe IR radiation received at the optical FPA unit, wherein saiddata-processing unit is configured to determine gas emission bycomparing data from a given frame with data from one or more priorframes.

In some embodiments, an infrared (IR) imaging system for quantifying oneor more parameters of a gas cloud is disclosed, the imaging systemcomprising: an optical system including an optical focal plane array(FPA) unit, the optical system having components defining at least twooptical channels thereof, said at least two optical channels beingspatially and spectrally different from one another, each of the atleast two optical channels positioned to transfer IR radiation incidenton the optical system towards the optical FPA unit; and adata-processing unit comprising one or more processors, saiddata-processing unit configured to acquire spectral optical data fromthe IR radiation received at the optical FPA unit, wherein saiddata-processing unit is configured to include an estimate of loss causedby a portion of said cloud being blown out of the field of view of theoptical system.

In some embodiments, an infrared (IR) imaging system for quantifying oneor more parameters of a gas cloud is disclosed, the imaging systemcomprising: an optical system including an optical focal plane array(FPA) unit, the optical system having components defining at least twooptical channels thereof, said at least two optical channels beingspatially and spectrally different from one another, each of the atleast two optical channels positioned to transfer IR radiation incidenton the optical system towards the optical FPA unit; and adata-processing unit comprising one or more processors, saiddata-processing unit configured to acquire spectral optical data fromthe IR radiation received at the optical FPA unit, wherein said opticalsystem and FPA unit together with said data-processing unit has adetection sensitivity for detecting absorption, and wherein saiddata-processing unit is configured to include an estimate of loss causedby a portion of said cloud having absorption less than the detectionsensitivity.

In some embodiments, an infrared (IR) imaging system for quantifying oneor more parameters of a gas cloud is disclosed, the imaging systemcomprising: an optical system including an optical focal plane array(FPA) unit, the optical system having components defining at least twooptical channels thereof, said at least two optical channels beingspatially and spectrally different from one another, each of the atleast two optical channels positioned to transfer IR radiation incidenton the optical system towards the optical FPA unit; and adata-processing unit comprising one or more processors, saiddata-processing unit configured to acquire spectral optical data fromthe IR radiation received at the optical FPA unit, wherein saiddata-processing unit is configured to use noise as a criteria fordetermining whether to de-emphasize or exclude data for a particularframe.

In some embodiments, an infrared (IR) imaging system for quantifying oneor more parameters of a gas cloud is disclosed, the imaging systemcomprising: an optical system including an optical focal plane array(FPA) unit, the optical system having components defining at least twooptical channels thereof, said at least two optical channels beingspatially and spectrally different from one another, each of the atleast two optical channels positioned to transfer IR radiation incidenton the optical system towards the optical FPA unit; and adata-processing unit comprising one or more processors, saiddata-processing unit configured to acquire spectral optical data fromthe IR radiation received at the optical FPA unit, wherein saiddata-processing unit is configured to determine a quantity of gas usingone or more specifications of the FPA unit, one or more specification ofthe optical system, distance of camera to the gas cloud, or combinationsthereof.

In some embodiments, a system for quantifying one or more parameters ofa gas cloud is disclosed, the system comprising: a communicationsubsystem for receiving optical data produced by a camera including anoptical focal plane array (FPA) unit, the camera having componentsdefining at least two optical channels thereof, said at least twooptical channels being spatially and spectrally different from oneanother, each of the at least two optical channels positioned totransfer IR radiation incident on the optical system towards the opticalFPA, said multi-spectral optical data derived from the IR radiationreceived at the optical FPA; and a data-processing unit comprising oneor more processors, said data-processing unit configured to acquire saidoptical data from said communication subsystem, wherein saiddata-processing unit is configured to determine gas emission bycomparing data from a given frame with data from one or more priorframes.

In some embodiments, a system for quantifying one or more parameters ofa gas cloud is disclosed, the system comprising: a communicationsubsystem for receiving optical data produced by a camera including anoptical focal plane array (FPA) unit, the camera having componentsdefining at least two optical channels thereof, said at least twooptical channels being spatially and spectrally different from oneanother, each of the at least two optical channels positioned totransfer IR radiation incident on the optical system towards the opticalFPA, said multi-spectral optical data derived from the IR radiationreceived at the optical FPA; and a data-processing unit comprising oneor more processors, said data-processing unit configured to acquire saidoptical data from said communication subsystem, wherein saiddata-processing unit is configured to include an estimate of loss causedby a portion of said cloud being blown out of the field of view of theoptical system.

In some embodiments, a system for quantifying one or more parameters ofa gas cloud is disclosed, the system comprising: a communicationsubsystem for receiving optical data produced by a camera including anoptical focal plane array (FPA) unit, the camera having componentsdefining at least two optical channels thereof, said at least twooptical channels being spatially and spectrally different from oneanother, each of the at least two optical channels positioned totransfer IR radiation incident on the optical system towards the opticalFPA, said multi-spectral optical data derived from the IR radiationreceived at the optical FPA; and a data-processing unit comprising oneor more processors, said data-processing unit configured to acquire saidoptical data from said communication subsystem, wherein said opticalsystem and FPA unit together with said data-processing unit has adetection sensitivity for detecting absorption, and wherein saiddata-processing unit is configured to include an estimate of loss causedby a portion of said cloud having absorption less than the detectionsensitivity.

In some embodiments, a system for quantifying one or more parameters ofa gas cloud is disclosed, the system comprising: a communicationsubsystem for receiving optical data produced by a camera including anoptical focal plane array (FPA) unit, the camera having componentsdefining at least two optical channels thereof, said at least twooptical channels being spatially and spectrally different from oneanother, each of the at least two optical channels positioned totransfer IR radiation incident on the optical system towards the opticalFPA, said multi-spectral optical data derived from the IR radiationreceived at the optical FPA; and a data-processing unit comprising oneor more processors, said data-processing unit configured to acquire saidoptical data from said communication subsystem, wherein saiddata-processing unit is configured to use noise as a criteria fordetermining whether to de-emphasize or exclude data for a particularframe.

In some embodiments, a system for quantifying one or more parameters ofa gas cloud is disclosed, the system comprising: a communicationsubsystem for receiving optical data produced by a camera including anoptical focal plane array (FPA) unit, the camera having componentsdefining at least two optical channels thereof, said at least twooptical channels being spatially and spectrally different from oneanother, each of the at least two optical channels positioned totransfer IR radiation incident on the optical system towards the opticalFPA, said multi-spectral optical data derived from the IR radiationreceived at the optical FPA; and a data-processing unit comprising oneor more processors, said data-processing unit configured to acquire saidoptical data from said communication subsystem, wherein saiddata-processing unit is configured to determine a quantity of gas usingone or more specifications of the FPA unit, one or more specification ofthe optical system, distance of camera to the gas cloud, or combinationsthereof.

In some embodiments, an infrared (IR) imaging system for quantifying oneor more parameters of a gas cloud is disclosed, the imaging systemcomprising: an optical system including an optical focal plane array(FPA) unit, the optical system having components defining at least twooptical channels thereof, said at least two optical channels beingspatially and spectrally different from one another, each of the atleast two optical channels positioned to transfer IR radiation incidenton the optical system towards the optical FPA unit; and adata-processing unit comprising one or more processors, saiddata-processing unit configured to acquire spectral optical data fromthe IR radiation received at the optical FPA unit, wherein saiddata-processing unit is configured to include an estimate of atmosphericabsorption between the gas cloud and the optical system.

In some embodiments, a method of analyzing a gas leak using a processoris disclosed, the method comprising: receiving a time series of datafrom a sensor, the data being capable of quantifying an absorptionspectrum of a gas cloud located within a field of view of the sensor,the data comprising a frame for each time in the time series, each framecomprising optical signal values corresponding to different locationswithin the field of view for each of a plurality of spectral wavelengthsof electromagnetic radiation; comparing a subsequent frame of data withat least one prior frame of data in the time series, analyzing at leastone property of a gas cloud located within the field of view of thesensor based on the comparison between the subsequent frame of data andthe at least one prior frame of data; and outputting an indicator of theat least one property of the gas cloud to a user interface.

In some embodiments, a method of analyzing the emission rate of a gasleak using a processor is disclosed, the method comprising: receiving atime series of data from a sensor, the data being capable of quantifyingan absorption spectrum of a gas cloud located within a field of view ofthe sensor, the data comprising a frame for each time in the timeseries, each frame comprising optical signal values corresponding todifferent locations within the field of view for each of a plurality ofspectral wavelengths of electromagnetic radiation; estimating the totalamount of gas within the field of view of the sensor; temporallysmoothing the estimate of the total amount of gas within the field ofview; combining the temporally-smoothed estimate of the total amount ofgas within the field of view with an estimate of the amount of gas thathas exited the field of view; combining the temporally-smoothed estimateof the total amount of detected gas within the field of view of thesensor with an estimate of the amount of gas that has dropped below thesensitivity limit of the sensor; and outputting an indicator of theemission rate of the gas cloud to a user interface.

In some embodiments, a system for analyzing a gas leak is disclosed, thesystem comprising: at least one processor; and a non-transitory memorywith instructions configured to cause the at least one processor toperform a method comprising: receiving a time series of data from asensor, the data being capable of quantifying an absorption spectrum ofa gas cloud located within a field of view of the sensor, the datacomprising a frame for each time in the time series, each framecomprising optical signal values corresponding to different locationswithin the field of view for each of a plurality of spectral wavelengthsof electromagnetic radiation; comparing a subsequent frame of data withat least one prior frame of data in the time series; analyzing at leastone property of a gas cloud located within the field of view of thesensor based on the comparison between the subsequent frame of data andthe at least one prior frame of data; and outputting an indicator of theat least one property of the gas cloud to a user interface.

In some embodiments, a system for analyzing the emission rate of a gasleak is disclosed, the system comprising: at least one processor; and anon-transitory memory with instructions configured to cause the at leastone processor to perform a method comprising: receiving a time series ofdata from a sensor, the data being capable of quantifying an absorptionspectrum of a gas cloud located within a field of view of the sensor,the data comprising a frame for each time in the time series, each framecomprising optical signal values corresponding to different locationswithin the field of view for each of a plurality of spectral wavelengthsof electromagnetic radiation; estimating the total amount of gas withinthe field of view of the sensor; temporally smoothing the estimate ofthe total amount of gas within the field of view; combining thetemporally-smoothed estimate of the total amount of gas within the fieldof view with an estimate of the amount of gas that has exited the fieldof view; combining the temporally-smoothed estimate of the total amountof detected gas within the field of view of the sensor with an estimateof the amount of gas that has dropped below the sensitivity limit of thesensor; and outputting an indicator of the emission rate of the gascloud to a user interface.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 provides a diagram schematically illustrating spatial andspectral division of incoming light by an embodiment of a dividedaperture infrared spectral imager (DAISI) system that can image anobject possessing IR spectral signature(s).

FIG. 2 illustrates another embodiment of a spectral imager system.

FIG. 3 illustrates an example of the measurement geometry for a gascloud imager (GCI).

FIG. 4 is a flowchart of an example method for calculating a runningaverage of a scene spectral distribution.

FIG. 5 is a flowchart of an example method for detecting a gas cloud.

FIG. 6 illustrates a gas cloud imager detector pixel projected to thelocation of the gas cloud.

FIG. 7 is a flowchart of an example method for calculating the absolutequantity of gas present in a gas cloud.

FIG. 8 is a flowchart of an example method for quantizing the emissionrate of a gas leak.

FIG. 9 is a flowchart of an example method 700 for compensating anestimate of emission rate based on gas exiting the field of view of thecamera and absorption dropping below sensitivity limits of the camera.

FIG. 10 illustrates a top view of an example scene measured by a gascloud imager camera, with the gas cloud at a distance z (left). FIG. 8also illustrates the example scene as viewed from the gas cloud imagercamera itself (right).

FIG. 11 shows an example of the gas cloud imager (GCI) live viewergraphical user interface.

FIG. 12 shows an example of the mosaic viewer interface which shows anoverview of the entire area being monitored.

FIG. 13 shows an example of the graphical user interface with an alarmcondition.

FIG. 14 shows an example of an alarm thresholds settings window.

FIG. 15 shows the measurement geometry for a single pixel in a gas cloudimager.

FIG. 16 shows an example absorption spectrum measurement for propylenegas, showing the measured spectrum M(λ).

FIG. 17 shows a detector pixel projected to the location of the gascloud.

DETAILED DESCRIPTION

A. Gas Cloud Imagers

Various embodiments of gas cloud imager (GCI) instruments are disclosedin U.S. patent application Ser. No. 14/538,827, filed Nov. 12, 2014, andentitled “DIVIDED-APERTURE INFRA-RED SPECTRAL IMAGING SYSTEM,” U.S.patent application Ser. No. 14/700,791, filed Apr. 30, 2015, andentitled “MOBIL GAS AND CHEMICAL IMAGING CAMERA,” and in U.S. patentapplication Ser. No. 14/700,567, filed Apr. 30, 2015, and entitled“DUAL-BAND DIVIDED-APERTURE INFRA-RED SPECTRAL IMAGING SYSTEM.” Each ofthe foregoing applications is hereby incorporated by reference herein inits entirety. The instruments disclosed in the foregoing applicationsare non-limiting examples of gas cloud imagers which may be used inconjunction with the algorithms disclosed herein.

By way of background, one type of gas cloud imager is a divided-apertureinfrared spectral imaging (DAISI) system that is structured and adaptedto provide identification of target chemical contents of the imagedscene. The system is based on spectrally-resolved imaging and canprovide such identification with a single-shot (also referred to as asnapshot) comprising a plurality of images having different wavelengthcompositions that are obtained generally simultaneously.

Without any loss of generality, snapshot refers to a system in whichmost of the data elements that are collected are continuously viewingthe light emitted from the scene. In contrast in scanning systems, atany given time only a minority of data elements are continuously viewinga scene, followed by a different set of data elements, and so on, untilthe full dataset is collected. Relatively fast operation can be achievedin a snapshot system because it does not need to use spectral or spatialscanning for the acquisition of infrared (IR) spectral signatures of thetarget chemical contents. Instead, IR detectors (such as, for example,infrared focal plane arrays or FPAs) associated with a plurality ofdifferent optical channels having different wavelength profiles can beused to form a spectral cube of imaging data. Although spectral data canbe obtained from a single snapshot comprising multiplesimultaneously-acquired images corresponding to different wavelengthranges, in various embodiments, multiple snap shots may be obtained. Invarious embodiments, these multiple snapshots can be averaged.Similarly, in certain embodiments multiple snap shots may be obtainedand a portion of these can be selected and possibly averaged.

Also, in contrast to commonly used IR spectral imaging systems, theDAISI system does not require cooling (for example cryogenic cooling).Accordingly, it can advantageously use uncooled infrared detectors. Forexample, in various implementations, the imaging systems disclosedherein do not include detectors configured to be cooled to a temperaturebelow 300 Kelvin. As another example, in various implementations, theimaging systems disclosed herein do not include detectors configured tobe cooled to a temperature below 273 Kelvin. As yet another example, invarious implementations, the imaging systems disclosed herein do notinclude detectors configured to be cooled to a temperature below 250Kelvin. As another example, in various implementations, the imagingsystems disclosed herein do not include detectors configured to becooled to a temperature below 200 Kelvin.

Implementations disclosed herein provide several advantages overexisting IR spectral imaging systems, most if not all of which mayrequire FPAs that are highly sensitive and cooled in order tocompensate, during the optical detection, for the reduction of thephoton flux caused by spectrum-scanning operation. The highly sensitiveand cooled FPA systems are expensive and require a great deal ofmaintenance. Since various embodiments disclosed herein are configuredto operate in single-shot acquisition mode without spatial and/orspectral scanning, the instrument can receive photons from a pluralityof points (e.g., every point) of the object substantiallysimultaneously, during the single reading. Accordingly, the embodimentsof imaging system described herein can collect a substantially greateramount of optical power from the imaged scene (for example, an order ofmagnitude more photons) at any given moment in time especially incomparison with spatial and/or spectral scanning systems. Consequently,various embodiments of the imaging systems disclosed herein can beoperated using uncooled detectors (for example, FPA unit including anarray of microbolometers) that are less sensitive to photons in the IRbut are well fit for continuous monitoring applications.

For example, in various implementations, the imaging systems disclosedherein do not include detectors configured to be cooled to a temperaturebelow 300 Kelvin. As another example, in various implementations, theimaging systems disclosed herein do not include detectors configured tobe cooled to a temperature below 273 Kelvin. As yet another example, invarious implementations, the imaging systems disclosed herein do notinclude detectors configured to be cooled to a temperature below 250Kelvin. As another example, in various implementations, the imagingsystems disclosed herein do not include detectors configured to becooled to a temperature below 200 Kelvin. Imaging systems includinguncooled detectors can be capable of operating in extreme weatherconditions, require less power, are capable of operation during day andnight, and are less expensive. Some embodiments described herein canalso be less susceptible to motion artifacts in comparison withspatially and/or spectrally scanning systems which can cause errors ineither the spectral data, spatial data, or both.

FIG. 1 provides a diagram schematically illustrating spatial andspectral division of incoming light by an embodiment 100 of a dividedaperture infrared spectral imager (DAISI) system that can image anobject 110 possessing IR spectral signature(s). The system 100 includesa front objective lens 124, an array of optical filters 130, an array ofreimaging lenses 128 and a detector array 136. In various embodiments,the detector array 136 can include a single FPA or an array of FPAs.Each detector in the detector array 136 can be disposed at the focus ofeach of the lenses in the array of reimaging lenses 128. In variousembodiments, the detector array 136 can include a plurality ofphoto-sensitive devices. In some embodiments, the plurality ofphoto-sensitive devices may comprise a two-dimensional imaging sensorarray that is sensitive to radiation having wavelengths between 1 μm and20 μm (for example, in near infra-red wavelength range, mid infra-redwavelength range, or long infra-red wavelength range). In variousembodiments, the plurality of photo-sensitive devices can include CCD orCMOS sensors, bolometers, microbolometers or other detectors that aresensitive to infra-red radiation. Without any loss of generality thedetector array 136 can also be referred to herein as an imaging systemor a camera.

An aperture of the system 100 associated with the front objective lenssystem 124 is spatially and spectrally divided by the combination of thearray of optical filters 130 and the array of reimaging lenses 128. Invarious embodiments, the combination of the array of optical filters 130and the array of reimaging lenses 128 can be considered to form aspectrally divided pupil that is disposed forward of the opticaldetector array 136. The spatial and spectral division of the apertureinto distinct aperture portions forms a plurality of optical channels120 along which light propagates. Various implementations of the systemcan include at least two spatially and spectrally different opticalchannels. For example, various implementations of the system can includeat least three, at least four, at least five, at least six, at leastseven, at least eight, at least nine, at least ten, at least eleven orat least twelve spatially and spectrally different optical channels. Thenumber of spatially and spectrally different optical channels can beless than 50 in various implementations of the system. In variousembodiments, the array 128 of re-imaging lenses 128 a and the array ofspectral filters 130 can respectively correspond to the distinct opticalchannels 120. The plurality of optical channels 120 can be spatiallyand/or spectrally distinct. The plurality of optical channels 120 can beformed in the object space and/or image space. The spatially andspectrally different optical channels can be separated angularly inspace. The array of spectral filters 130 may additionally include afilter-holding aperture mask (comprising, for example, IR light-blockingmaterials such as ceramic, metal, or plastic).

Light from the object 110 (for example a cloud of gas), the opticalproperties of which in the IR are described by a unique absorption,reflection and/or emission spectrum, is received by the aperture of thesystem 100. This light propagates through each of the plurality ofoptical channels 120 and is further imaged onto the optical detectorarray 136. In various implementations, the detector array 136 caninclude at least one FPA. In various embodiments, each of the re-imaginglenses 128 a can be spatially aligned with a respectively-correspondingspectral region. In the illustrated implementation, each filter elementfrom the array of spectral filters 130 corresponds to a differentspectral region. Each re-imaging lens 128 a and the corresponding filterelement of the array of spectral filter 130 can coincide with (or form)a portion of the divided aperture and therefore withrespectively-corresponding spatial channel 120. Accordingly, in variousembodiments an imaging lens 128 a and a corresponding spectral filtercan be disposed in the optical path of one of the plurality of opticalchannels 120. Radiation from the object 110 propagating through each ofthe plurality of optical channels 120 travels along the optical path ofeach re-imaging lens 128 a and the corresponding filter element of thearray of spectral filter 130 and is incident on the detector array(e.g., FPA component) 136 to form a single image (e.g., sub-image) ofthe object 110.

The image formed by the detector array 136 generally includes aplurality of sub-images formed by each of the optical channels 120. Eachof the plurality of sub-images can provide different spatial andspectral information of the object 110. The different spatialinformation results from some parallax because of the different spatiallocations of the smaller apertures of the divided aperture. In variousembodiments, adjacent sub-images can be characterized by close orsubstantially equal spectral signatures.

The detector array (e.g., FPA component) 136 is further operablyconnected with a data-processing unit that includes a processor 150 (notshown). The processor can comprise processing electronics. Thedata-processing unit can be located remotely from the detector array136. For example, in some implementations, the data-processing unit canbe located at a distance of about 10-3000 feet from the detector array136. As another example, in some other implementations, thedata-processing unit can be located at a distance less than about 10feet from the detector array 136 or greater than about 3000 feet. Thedata-processing unit can be connected to the detector array by a wiredor a wireless communication link. The detector array (e.g., FPAcomponent) 136 and/or the data-processing unit can be operably connectedwith a display device.

The processor or processing electronics 150 can be programmed toaggregate the data acquired with the system 100 into a spectral datacube. The data cube represents, in spatial (x, y) and spectral (λ)coordinates, an overall spectral image of the object 110 within thespectral region defined by the combination of the filter elements in thearray of spectral filters 130. Additionally, in various embodiments, theprocessor or processing electronics 150 may be programmed to determinethe unique absorption characteristic of the object 110. Also, theprocessor 150 can, alternatively or in addition, map the overall imagedata cube into a cube of data representing, for example, spatialdistribution of concentrations, c, of targeted chemical componentswithin the field of view associated with the object 110.

The Processor

Various implementations of the embodiment 100 can include an optionalmoveable temperature-controlled reference source 160 including, forexample, a shutter system comprising one or more reference shuttersmaintained at different temperatures. The reference source 160 caninclude a heater, a cooler or a temperature-controlled elementconfigured to maintain the reference source 160 at a desiredtemperature. For example, in various implementations, the embodiment 100can include two reference shutters maintained at different temperatures.In various implementations including more than one reference shutter,some of the shutters may not be temperature controlled. The referencesource 160 is removably and, in one implementation, periodicallyinserted into an optical path of light traversing the system 100 fromthe object 110 to the detector array (e.g., FPA component) 136 along atleast one of the channels 120. The removable reference source 160 thuscan block such optical path. Moreover, this reference source 160 canprovide a reference IR spectrum to recalibrate various componentsincluding the detector array 136 of the system 100 in real time.

In the embodiment 100 illustrated in FIG. 1, the front objective lenssystem 124 is shown to include a single front objective lens positionedto establish a common field-of-view (FOV) for the reimaging lenses 128 aand to define an aperture stop for the whole system. In this specificcase, the aperture stop substantially spatially coincides with and/or isabout the same size or slightly larger, as the plurality of smallerlimiting apertures corresponding to different optical channels 120. As aresult, the positions for spectral filters of the different opticalchannels 120 coincide with the position of the aperture stop of thewhole system, which in this example is shown as a surface between thelens system 124 and the array 128 of the reimaging lenses 128 a. Invarious implementations, the lens system 124 can be an objective lens124. However, the objective lens 124 is optional and various embodimentsof the system 100 need not include the objective lens 124. In variousembodiments, the objective lens 124 can slightly shift the imagesobtained by the different detectors in the array 136 spatially along adirection perpendicular to optical axis of the lens 124, thus thefunctionality of the system 100 is not necessarily compromised when theobjective lens 124 is not included. Generally, however, the fieldapertures corresponding to different optical channels may be located inthe same or different planes. These field apertures may be defined bythe aperture of the reimaging lens 128 a and/or filters in the dividedaperture 130 in certain implementations. In one implementation, thefield apertures corresponding to different optical channels can belocated in different planes and the different planes can be opticalconjugates of one another. Similarly, while all of the filter elementsin the array of spectral filters 130 of the embodiment 100 are shown tolie in one plane, generally different filter elements of the array ofspectral filter 130 can be disposed in different planes. For example,different filter elements of the array of spectral filters 130 can bedisposed in different planes that are optically conjugate to oneanother. However, in other embodiments, the different filter elementscan be disposed in non-conjugate planes.

In various implementations, the front objective lens 124 need not be asingle optical element, but instead can include a plurality of lenses224 as shown in an embodiment 200 of the DAISI imaging system in FIG. 2.These lenses 224 are configured to divide an incoming optical wavefrontfrom the object 110. For example, the array of front objective lenses224 can be disposed so as to receive an IR wavefront emitted by theobject that is directed toward the DAISI system. The plurality of frontobjective lenses 224 divide the wavefront spatially into non-overlappingsections. FIG. 2 shows three objective lenses 224 in a front opticalportion of the optical system contributing to the spatial division ofthe aperture of the system in this example. The plurality of objectivelenses 224, however, can be configured as a two-dimensional (2D) arrayof lenses.

FIG. 2 presents a general view of the imaging system 200 and theresultant field of view of the imaging system 200. An exploded view 202of the imaging system 200 is also depicted in greater detail in a figureinset of FIG. 2. As illustrated in the detailed view 202, the embodimentof the imaging system 200 includes a field reference 204 at the frontend of the system. The field reference 204 can be used to truncate thefield of view. The configuration illustrated in FIG. 2 has anoperational advantage over embodiment 100 of FIG. 1 in that the overallsize and/or weight and/or cost of manufacture of the embodiment 200 canbe greatly reduced because the objective lens is smaller. Each pair ofthe lenses in the array 224 and the array 128 is associated with a fieldof view (FOV). Each pair of lenses in the array 224 and the array 128receives light from the object from a different angle. While the lenses224 are shown to be disposed substantially in the same plane, optionallydifferent objective lenses in the array of front objective lenses 224can be disposed in more than one plane. For example, some of theindividual lenses 224 can be displaced with respect to some otherindividual lenses 224 along the axis 226 (not shown) and/or havedifferent focal lengths as compared to some other lenses 224. Asdiscussed below, the field reference 204 can be useful in calibratingthe multiple detectors 236.

In one implementation, the front objective lens system such as the arrayof lenses 224 is configured as an array of lenses integrated or moldedin association with a monolithic substrate. Such an arrangement canreduce the costs and complexity otherwise accompanying the opticaladjustment of individual lenses within the system. An individual lens224 can optionally include a lens with varying magnification. As oneexample, a pair of thin and large diameter Alvarez plates can be used inat least a portion of the front objective lens system. Without any lossof generality, the Alvarez plates can produce a change in focal lengthwhen translated orthogonally with respect to the optical beam.

Referring to FIG. 1, the detector array 136 (e.g., FPA component)configured to receive the optical data representing spectralsignature(s) of the imaged object 110 can be configured as a singleimaging array (e.g., FPA) 136. This single array may be adapted toacquire more than one image (formed by more than one optical channel120) simultaneously. Alternatively, the detector array 136 may include aFPA unit. In various implementations, the FPA unit can include aplurality of optical FPAs. At least one of these plurality of FPAs canbe configured to acquire more than one spectrally distinct image of theimaged object. For example, as shown in the embodiment 200 of FIG. 2, invarious embodiments, the number of FPAs included in the FPA unit maycorrespond to the number of the front objective lenses 224. In theembodiment 200 of FIG. 2, for example, three FPAs 236 are providedcorresponding to the three objective lenses 224. In one implementationof the system, the FPA unit can include an array of microbolometers. Theuse of multiple microbolometers advantageously allows for an inexpensiveway to increase the total number of detection elements (i.e. pixels) forrecording of the three-dimensional data cube in a single acquisitionevent (i.e. one snapshot). In various embodiments, an array ofmicrobolometers more efficiently utilizes the detector pixels of thearray of FPAs (e.g., each FPA) as the number of unused pixels isreduced, minimized and/or eliminated between the images that may existwhen using a single microbolometer. The optical filters, used in variousimplementations of the system, that provide spectrally-distinct IR image(e.g., sub-image) of the object can employ absorption filters,interference filters, and Fabry-Perot etalon based filters, to name justa few. When interference filters are used, the image acquisition throughan individual imaging channel defined by an individual re-imaging lens(such as a lens 128 a of FIGS. 1 and 2) may be carried out in a singlespectral bandwidth or multiple spectral bandwidths.

The optical filtering configuration of various embodiments disclosedherein may advantageously use a bandpass filter having a specifiedspectral band. The filters may be placed in front of the optical FPA (orgenerally, between the optical FPA and the object). In implementationsof the system that include microbolometers, the predominant contributionto noise associated with image acquisition can be attributed to detectornoise. To compensate and/or reduce the noise, various embodimentsdisclosed herein utilize spectrally-multiplexed filters. In variousimplementations, the spectrally-multiplexed filters can comprise aplurality of long pass (LP) filters, a plurality of band pass filtersand any combinations thereof. A LP filter generally attenuates shorterwavelengths and transmits (passes) longer wavelengths (e.g., over theactive range of the target IR portion of the spectrum). In variousembodiments, short-wavelength-pass (SP) filters, may also be used. A SPfilter generally attenuates longer wavelengths and transmits (passes)shorter wavelengths (e.g., over the active range of the target IRportion of the spectrum). At least in part due to thesnap-shot/non-scanning mode of operation, embodiments of the imagingsystem described herein can use less sensitive microbolometers withoutcompromising the SNR. The use of microbolometers, asdetector-noise-limited devices, in turn not only benefits from the useof spectrally multiplexed filters, but also does not require cooling ofthe imaging system during normal operation.

As discussed above, various embodiments may optionally, and in additionto a temperature-controlled reference unit (for example temperaturecontrolled shutters such as shutter 160), employ a field referencecomponent, or an array of field reference components (e.g., filedreference apertures), to enable dynamic calibration. Such dynamiccalibration can be used for spectral acquisition of one or more or everydata cube. Such dynamic calibration can also be used for aspectrally-neutral camera-to-camera combination to enable dynamiccompensation of parallax artifacts. The use of thetemperature-controlled reference unit (for example,temperature-controlled shutter system 160) and field-referencecomponent(s) facilitates maintenance of proper calibration of each ofthe FPAs individually and the entire FPA unit as a whole.

In particular, and in further reference to FIGS. 1 and 2, thetemperature-controlled unit generally employs a system having first andsecond temperature zones maintained at first and second differenttemperatures. For example, shutter system of each of the embodiments 100and 200 can employ not one but at least two temperature-controlledshutters that are substantially parallel to one another and transverseto the general optical axis 226 of the embodiment(s) 100 and 200. Twoshutters at two different temperatures may be employed to provide moreinformation for calibration; for example, the absolute value of thedifference between FPAs at one temperature as well as the change in thatdifference with temperature change can be recorded. As discussed above,only one of the two shutters can be temperature controlled in variousimplementations while the other is not. In various implementations,multiple shutters can be employed to create a known referencetemperature difference perceived by the FPA. This reference temperaturedifference is provided by the IR radiation emitted by the multipleshutters when they are positioned to block the radiation from the object110. As a result, not only the offset values corresponding to each ofthe individual FPAs pixels can be adjusted but also the gain values ofthese FPAs. In an alternative embodiment, the system having first andsecond temperature zones may include a single or multi-portion piece.This single or multi-portion piece may comprise for example a plate.This piece may be mechanically-movable across the optical axis with theuse of appropriate guides and having a first portion at a firsttemperature and a second portion at a second temperature.

Various implementations of the DAISI system can include a variety oftemperature calibration elements to facilitate dynamic calibration ofthe FPAs. The temperature calibration elements can include mirrors aswell as reference sources. The use of optically-filtered FPAs in variousembodiments of the system described herein can provide a system withhigher number of pixels. For example, embodiments including a singlelarge format microbolometer FPA array can provide a system with largenumber of pixels. Various embodiments of the systems described hereincan also offer a high optical throughput for a substantially low numberof optical channels. For example, the systems described herein canprovide a high optical throughput for a number of optical channelsbetween 4 and 50. By having a lower number of optical channels (e.g.,between 4 and 50 optical channels), the systems described herein havewider spectral bins which allows the signals acquired within eachspectral bin to have a greater integrated intensity.

B. Gas Leak Quantification with a Gas Cloud Imager

The idea of using passive infrared absorption spectroscopy to detect andanalyze gas clouds is an idea that has been pursued for decades, butwhose implementation in an autonomous setting has remained out of reach.The primary difficulty with adapting these instruments to industrial usehas been their low data rate—gas clouds are dynamic phenomena andrequire video analytics to properly detect them. As discussed herein,recently, advanced spectral imaging instruments have become availablethat improve light collection capacity and allow for video-rate imaging.Even with these new instruments, however, existing computational methodsare incapable of performing autonomous operation, as they requiresupervision from an operator in order to function. In the discussionbelow, we provide alternative methods for detection and quantificationof gas clouds that allow fully autonomous operation.

1. Conventional Measurement Model

For a passive infrared sensor, the typical gas cloud measurement modelis a three-layer radiative transfer system, in which the ray path isdivided into three regions: (1) a layer of atmosphere between the sensorand the gas cloud, (2) a layer containing one or more of the targetgases, and (3) an atmosphere behind the gas. Layer (3) is followed by aradiation source, which may either be an opaque surface or the skyitself. In the following discussion, we use the following definitions:

L_(f), L_(b), L_(s): radiances originating from foreground, background,and source layers

τ_(f), τ_(b), τ_(c): transmission of foreground, background, and cloudlayers

T_(f′), T_(b), T_(c): temperatures of foreground, background, and cloudlayers

M⁽⁰⁾, M⁽¹⁾: at-sensor radiance in the absence (0) or presence (1) of thecloud

σ_(m): absorption cross-section of target gas m

η_(m): concentration of target gas m

l: path length through the gas cloud

FIG. 3 illustrates an example of the measurement geometry for a gascloud imager (GCI). As just discussed, the field of view of each pixel(with line of sight indicated by “LOS”) is divided into three layers andan external source.

A spectral imager measures the at-sensor radiance given by the lineintegral of the light extending from the source, through each of thethree layers of the system (see FIG. 3). When no gas cloud is present,radiative transfer of a ray along the line of sight givesM ⁽⁰⁾ =L _(f)+τ_(f) L _(b)+τ_(f) T _(b) L _(s).When a gas cloud is present, this becomesM ⁽¹⁾ =L _(f)+τ_(f)(1−τ_(c))B(T _(c))+τ_(f)τ_(c) L _(b)+τ_(f)τ_(c)τ_(b)L _(s).Subtracting M⁽⁰⁾ from M⁽¹⁾ gives the radiance difference in the presenceof the target gas cloud:ΔM

M ⁽¹⁾ −M ⁽⁰⁾=−τ_(f)(1−τ_(c))[L _(b)+τ_(b) L _(s) −B(T _(c))],  (1)where ΔL, the term [L_(b)+τ_(b) L_(s)−B(T_(c))], is the “thermalradiance contrast,” the sign of which indicates whether the cloud isobserved in emission (ΔL<0) or absorption (ΔL>0). When the backgroundmay be approximated as a homogeneous layer at thermal equilibrium, wecan further write that L_(b)=(1−τ_(b)) B(T_(b)). Note that all of thesequantities have an implicit spectral dependence (i.e. M⁽⁰⁾≡M⁽⁰⁾(λ)etc.).

Thus, if we measure the change in at-sensor radiance, ΔM, and we canestimate the thermal radiance contrast ΔL and foreground transmissionτ_(f), then we can obtain the gas cloud transmission τ_(c) as1−τ_(c) =−ΔM/(τ_(f) ΔL)  (2)When the gas concentration is low, the transmission can be modeled witha linearized version of the Beer-Lambert equation obtained by Taylorexpansion:

$\begin{matrix}{{1 - \tau_{c}} = {{1 - e^{\alpha_{c}}} = {{\alpha_{c} + {\frac{1}{2!}\alpha_{c}^{2}} + \ldots}\; \approx \alpha_{c}}}} & (3)\end{matrix}$for absorbance α_(c). For a single gas, the absorbance can be written interms of the absorption cross-section σ, the number density (or“concentration”) n, and the path length l through the layer asα_(c)=σnl. Using (3) to substitute this into (2) gives

$\begin{matrix}{{{nl} \approx \frac{\Delta\; M}{\tau_{f}\sigma\;\Delta\; L}},} & (4)\end{matrix}$where the left hand side represents the quantity we want to know—theconcentration×path length, or “column density.”

In order to use (4), the approach taken in the existing literature isgenerally the following. First we either take τ_(f)=1; τ_(b)=1 or theoperator provides independent estimates of the transmission spectraτ_(f)(λ) and τ_(b)(λ). The gas absorption cross-section spectrum σ(λ) iseasily obtained from a spectral library. The remaining unknowns areT_(b), L_(s), and T_(c). The temperature of the gas cloud T_(c) and theatmosphere behind it T_(b) are often taken as being the same andestimated by the operator using an independent measurement of the airtemperature. Finally, the source radiance L_(s) is generally taken to beeither a greybody (if the background is an opaque surface) or isestimated from radiative transfer modelling software, such as MODTRAN.

2. General Approach for Autonomous Operation

The computational approach proceeds as follows:

1. Rather that attempting to estimate the absolute quantity of the gaspresent in a scene, we attempt to estimate the change in the gas,relative to either an initial time or to a running average. This allowsfor a simplification of the measurement model, so that many of theunknown quantities no longer need to be estimated.

2. We have found that using a running average of the scene is importantnot only for gas detection (as in the step above) but also fordiscriminating moving objects (such as people, cars, birds, etc.) frompotential gas clouds. Some care must be taken when calculating therunning mean, however, in order to prevent gas clouds and moving objectsfrom “burning in” their signal into the running mean.

3. From the difference between the current frame's radiance spectrum tothat of the running mean, we can calculate the absorption spectrum ateach pixel. From the absorption spectrum, we can estimate the gas columndensity by either averaging the absorption over a few selected bands orby fitting the cross-section spectrum to the measured absorption value.

4. If the distance to the gas cloud is known or can be estimated by thecamera, then we can scale the detected gas column density (ppm·m units)into absolute quantity units (kg). Summing over all pixels in the scenetherefore gives an estimate of the total gas quantity (in kg) within thecloud at a given time.

5. In order to estimate total emission, one cannot simply use the valueobtained in the previous step (the total gas quantity at a singlesnapshot in time), since the same cloud can be obtained by either a slowleak into an environment with little wind, or a fast leak into anenvironment with strong wind conditions. Rather, total emission isbetter measured by first estimating the emission rate over a period oftime, and then integrating over that time period to get the total gasemission.

6. For the gas emission rate, we start by taking a running average ofthe total detected gas in a scene. We then use a heuristic method forestimating how much of the gas cloud in the previous frame we expect tohave lost measurement sensitivity to, and add that value to the currentframe's total gas volume. Finally, if we have knowledge of the winddirection and speed relative to the camera's pointing direction, then wecan easily estimate how much gas is left in the field of view in theprevious frame. This value is also added to the current frame's totalgas volume. If we take this “augmented” estimate of the current frame'stotal gas volume, any changes in this value (if positive) indicateemission.

7. If we monitor a gas cloud over a period of time and sum the emissionrate over the monitor period, we have an estimate for the total gasquantity emitted.

3. New Measurement Model

As shown above, the conventional method uses a number of steps in whichan operator must manually specify quantities in order for thecomputation to proceed. This type of method cannot be performedautonomously under conditions of changing weather, temperature, etc. Italso makes the assumption that the source (if an opaque surface) is agreybody—an assumption that we see violated in much of our own testing.We develop an alternative model that does not require these assumptionsfor the measurement to proceed. Rather than attempting to measure theabsolute gas absorption spectrum ΔM(λ), we instead measure only thechange in the spectrum, with respect to either an initial measurement,or with respect to a running average of the scene. This allows us todrop all of the background layer from the measurement model, so that theno-gas at-sensor radiance, with-gas at-sensor radiance, and theirdifference are nowM ⁽⁰⁾ =L _(f)+τ_(f) L _(s)M ⁽¹⁾ =L _(f)τ_(f)(1−τ_(c))B(T _(c))+τ_(f)τ_(c) L _(s)ΔM=M ⁽¹⁾ −M ⁽⁰⁾=τ_(f)(1−τ_(c))[B(T _(c))−L _(s)],

If we ignore the path absorption in the foreground (i.e. set τ_(f)=1),then the at-sensor radiance without gas is now equal to the sourceradiance (M⁽⁰⁾

L_(s)), so that solving for the gas transmission gives

$\begin{matrix}{{{{1 - \tau_{c}} \approx \alpha_{c}} = \frac{M^{(1)} - M^{(0)}}{{B\left( T_{c} \right)} - M^{(0)}}},} & (5)\end{matrix}$Here we can interpret the quantity M⁽⁰⁾(λ) as being either the at-sensorradiance spectrum measured at an initial time, or as a running mean ofthe at-sensor radiance, so that what we choose to measure will befluctuations about a mean value. Since gas clouds on this scale aredynamic and fast-moving phenomena, this method still produces excellentgas cloud detection, as we will show below. Finally, for estimation ofthe gas column density nl from measurements, we use

$\begin{matrix}{{{nl} = \frac{M^{(1)} - M^{(0)}}{\sigma\left\lbrack {{B\left( T_{c} \right)} - M^{(0)}} \right\rbrack}},} & (6)\end{matrix}$

4. Calculating a Running Average of a Scene

Experimentally, we have found that using a running average of the scenespectral distribution

M(x, y, λ, t)

_(t) provides much better results than using the scene spectraldistribution at an initial time M(x, y, λ, t₀) From here on, we willrefer to the scene spectral distribution as the scene “datacube”Calculating the running average comprises several steps, as illustratedin FIG. 4, which is a flowchart of an example method 400 for calculatinga running average of the scene spectral distribution:

1. First, as illustrated in block 410, the system needs to acquire aninitial estimate of the scene reference datacube M⁽⁰⁾(x,y,λ). For thiswe simply collect a sequence of datacubes of the scene and average themtogether. Until a reliable initial estimate is formed, the system cannotattempt gas cloud detection, since the results are no more reliable thanthe reference datacube is.

2. After the initial estimate of M⁽⁰⁾(x,y,λ) is formed, as illustratedin block 420, we can add subsequent datacubes into our running averageusing the well-known updating algorithm (given here in pseudocode):Δx=x _(i) −x   (a)x+=Δx/i  (b)where x is the quantity to average (such as the scene datacube),x_(mean) is its running mean, and i is the frame counter (i.e. if thecurrent frame is the 15th, then i=14, since the counter starts at zero.

3. While the simple running average improves detection, over what can beachieved with a simple initial estimate that is not updated, problemscan occur as a result of moving objects in the scene. For example, if acar drives through the scene, the radiance of the car is likely to bequite different from that of the radiance of the scene behind the car(and now being blocked by the car). Since the car will soon exit thatregion of the scene, leaving the original background exposed once more,it will degrade performance of the system if it were allowed to changethe reference datacube. Since moving objects generally cause largesignal changes, a powerful method to mitigate their effect on thereference datacube is to allow the moving average update to occur onlyif a given pixel experiences a small signal change and not a large one.Empirically, what we have found to work best is to place a threshold onthe estimated SNR of a pixel: if a pixel's estimated SNR value is above2.5, do not use the current frame to update that pixel in the referencedatacube. If a pixel's estimated SNR is below 2.5, then go ahead andallow it to be updated.

4. This method therefore uses a running estimate of the SNR, which iscalculated as follows. Along with the algorithm that continuouslyupdates the reference datacube with each new frame, we also calculateand continuously update an estimated variance with each new frame, asillustrated in blocks 430 and 440. The above algorithm therefore becomesΔx=x _(i) −x   (a)x _(mean) +=Δx/i  (b)m ₂ +=Δx*(x−x _(mean))  (c)var_(x) =m ₂/(i−1)  (d)SNR _(x)=(x−x _(mean))/√{square root over (var_(x))}  (e)where var_(x) is the estimated variance for the pixel at the currentframe, √{square root over (var_(x))} is the corresponding estimatedstandard deviation. Thus, as illustrated in block 450, for any pixelwhose SNR value is above the threshold (we typically use 2.5), theprevious frame's value at that pixel is the one used in the “updated”reference datacube. For any pixel whose SNR is at or below thethreshold, the above algorithm applies the update (i.e. it uses the newvalue for x_(mean) rather than the previous frame's x_(mean) for thepixel's value in the reference datacube).

5. Calculating the Absorption, Gas Column Density, and Absolute Quantityof Gas

FIG. 5 is a flowchart of an example method 500 for detecting a gascloud. For passive absorption spectroscopy, measuring the absorption bya gas requires knowing the quantity of light reaching the sensor bothwith and without the gas. For autonomous measurement, since we can neverensure that we have available a measurement in which no gas is present,we instead attempt to measure only the changes in the gas concentration,rather than the absolute concentration values, as illustrated in block510. Thus, the absorption spectrum at a pixel is given by (5), whereM⁽⁰⁾ represents the reference datacube, M⁽¹⁾ is the datacube obtained inthe current frame, B(T_(c)) is the Planck blackbody spectrum attemperature T_(c), and T_(c) is the gas cloud temperature. As shown inblock 520, from the absorption spectrum at a pixel, we can performspectral matching to estimate the probability that the absorptionindicates presence of a gas. If the gas detection algorithm indicatesthat there is a high probability of there being a gas cloud at a givenpixel, then we can go to the next step and calculate the gas columndensity at the pixel.

As shown in block 530, there are two basic techniques for estimating thegas column density. The first technique is to average the absorptionover one or more spectral bands in which the gas absorptioncross-section is significant (i.e. not close to zero). A secondtechnique is to use a statistical method to fit the gas cross-sectionspectrum to the measured absorption spectrum. Both of these techniqueswork, with the former requiring less computation, and the latter beingmore accurate but also more in need of regularization. Once we have thecolumn density (in, say, units of ppm·m), the next step is to convertthe measurement units to an absolute quantity. In order to convert ameasurement in ppm·m units to one in ppm·m³ units, we need onlycalculate the effective area of a pixel projected onto the gas cloud.

FIG. 6 illustrates a gas cloud imager detector pixel projected to thelocation of the gas cloud. Using the known dimensions of the detectorarray pixels (p_(x), p_(y)), the focal length f of the objective lens,and the gas cloud distance z, we can calculate the projected dimensionof the pixel at the plane of the gas cloud as

$\frac{P_{x}}{z} = {\left. \frac{p_{x}}{f}\rightarrow P_{x} \right. = {p_{x}{z/{f.}}}}$Since most detectors have p_(x)=p_(y), we can write that the projectedarea of the pixel is thereforeA _(proj)=(p _(x) z/f)²  (7)

FIG. 7 is a flowchart of an example method 700 for calculating theabsolute quantity of gas present in a gas cloud. While the pixeldimension p_(x) and f are known as a result of the hardware design, thegas cloud distance z varies and must be estimated. When setting up a gascloud imaging camera at a facility, one of the early setup procedures isto measure the distances from the camera to the primary items to bemonitored. These items are often things such as a collection of tightlyinterwound pipes, the wall of a gas container tank, the opening of a gasseparator tank, etc. The important thing is that the general region inwhich potential leaks may occur is known a priori, and thus the distanceto any gas leak can be estimated to reasonable accuracy by using thatdistance as measured during the system setup. As shown in block 710,with distance z known, we can apply (7) to scale the measured gas columndensity to absolute units. As shown in block 720, simple multiplicationleads to units of ppm·m³. But, as shown in block 730, multiplying thisresult by the number of molecules per cubic meter in standardatmospheric temperature and pressure, and then dividing by 1×10⁶(because the units is parts per million), we now have a measurement inunits of numbers of gas molecules. Since each gas has a known molecularweight, we can also convert “number of gas molecules” directly tokilograms, as shown in block 740, or equivalently to an equivalentvolume of pure gas at atmospheric pressure (e.g. units of m³), as shownin block 750.

This calculation gives the absolute gas quantity at each pixel in theimage, and if we sum over all pixels in the image we obtain the totalvolume of gas at one snapshot in time.

While the distance to the gas cloud can be estimated by assuming thatthe cloud will occur near the equipment being monitored. There are othertechniques which are also available. One can use multiple infraredcameras viewing the same scene to triangulate on the gas cloud. Anothermethod is the use a laser tracker (or “laser range finder”) tuned to awavelength that is absorbed by the gas.

6. Emission Rate Quantization

FIG. 8 is a flowchart of an example method 800 for quantizing theemission rate of a gas leak. As shown in block 810, the method beginswith an estimate of the quantity of gas present at each pixel of theimage (which can be determined using the method illustrated in FIG. 5).At block 820, the total volume of gas present in the image can becalculated by summing over all pixels in the frame.

From the previous step, we know the total amount of gas in the sceneduring each measurement frame. As shown in block 840, from a safetyperspective, this measure of the gas volume, and an estimate of itsconcentration (not column density) are the two most important measures.The former determines the scale of the danger, and the latter determineswhether the cloud is capable of igniting. If we are using the gas cloudimager not for safety monitoring but for environmental monitoring or forgas leak detection and repair (LDAR), then the primary quantities ofinterest are emission rate (units of kg/hr, for example) and totalemission (units of kg). At block 830, the emission rate and/or totalemission of the gas leak can be calculated. Estimating these quantitiesrequires some additional work.

Researchers have attempted to estimate gas emission rates from gas cloudimaging, but all of the currently published work of which we are awareuse supervised methods. That is, they use optical flow techniques toestimate the speed of each tiny parcel of gas within the gas cloud, drawa line or a box somewhere in the image such that the leak source is onone side, and all of the gas passes across the line or box. Not only isthis method unsatisfactory from the point of view that it incorporatesuser supervision or some kind of prior knowledge about the location ofthe leak source, but optical flow techniques are also computationallyintensive and require special care when working with noisy data. Wedevelop a new method that is computationally easy, requires nosupervision or knowledge of the leak source location, and can work withsurprisingly noisy data.

As shown at block 850, with low-noise data, one could measure the amountof gas present in each frame of a video sequence, and then say that anyincrease in the gas indicates an emission source. For noisy data, onecan use temporal smoothing and look for changes in the temporallysmoothed value for total gas present in the scene. Thus, in principle,one need only monitor the steady increase in total gas from thebeginning to end of the monitoring period. However, two competingeffects work against this. If there is wind in the scene, or if the gasis moving rapidly, then part of the gas cloud may exit the field of viewand reduce the total amount of gas in the scene. If this were to happenwhile a leak were constantly emitting new gas, then the two wouldcompete for each other and the net effect would be no change in totalgas observed, and zero estimated gas emission. Thus, we will need tocompensate for any gas that leaves the field of view. Secondly, anothereffect is that some of the gas will drop below the sensitivity limit ofthe camera. If, for example, there were a momentary leak that created astationary gas cloud within the scene. As the gas cloud slowlydissipates by mixing with the ambient air, losing concentration butgrowing in size, the gas cloud imager will lose sensitivity to the lowerconcentrations and will see a steady decline in the total gas, eventhough none of it has left the field of view. Clearly, we need tocompensate for this effect as well in order to get accurate estimates ofgas emission rates.

FIG. 9 is a flowchart of an example method 900 for compensating anestimate of emission rate based on gas exiting the field of view of thecamera and absorption dropping below sensitivity limits of the camera.As shown at block 910, A temporally-smoothed moving average of the totalgas in the scene is efficiently implemented using anexponentially-weighted mean average (EWMA). Using the EWMA the measuredgas volume as our best estimate of the true gas volume in the scene, atblock 940, we next add our estimate of the amount of gas lost by exitingthe field of view (calculated at block 920), and also the amount of gaslost due to dropping below our sensitivity limit (calculated at block930). From this “augmented” estimate of the current frame's total gasvolume, we estimate the emission rate as the amount by which this gasvolume has increased since the last frame, as shown at block 950. Ifthis (augmented) gas volume has decreased, then we say that theestimated emission is zero. (That is, the estimate is biased to acceptonly positive values.)

Estimating the amount of gas that we expect to lose detection to by thetime of the next frame is determined using a simple heuristic model thatis adjusted to match experimental data. In the model, we first calculatethe range of gas column density values detected within the gas cloud. Athreshold is set to be some fraction of the range of ppm·m values abovethe minimum detected value. Thus, if the maximum ppm·m value detectedwithin a gas cloud were calculated as 5000 ppm·m, and the lowest valuewere 100 ppm·m, then the range would be 4900 ppm·m. If we set athreshold as 20% of the range, then the threshold in units of ppm·mwould be(ppm·m threshold)=(minimum ppm·m)+0.2 (ppm·m range)=100+0.2(4900)=1080.Next we locate the set of all “edge pixels” in the gas cloud—all pixelsthat lie no more than two pixels away from a pixel without gas detected.We expect that some fraction of edge pixels whose column density liesbelow the calculated threshold will drop below the detection limit ofthe camera. Using experimental data, we determined that the best valuefor our camera was 0.25. (As we will see, the final result is usuallynot very sensitive to the values chosen for use in this heuristicmodel.) So, say we find all of the edge pixels that lie below thethreshold, sum up all of their ppm·m values, and multiply the result by0.25. This is the total amount of gas we expect to lose sensitivity toby the next frame. Store that value at block 930. When we try toestimate the total gas present in a frame, we will augment it using thisvalue.

The next step attempts to estimate how much gas will exit the field ofview. This either requires knowing the wind speed and direction in termsof the gas cloud imager's optical axis, or using video analytics toestimate the speed of motion of the gas. FIG. 8 illustrates a top viewof an example scene measured by a gas cloud imager camera, with the gascloud at a distance z (left). FIG. 10 also illustrates the example sceneas viewed from the gas cloud imager camera itself (right). The hatchedregion at the right hand side of the image indicates the area in whichany detected gas is expected to leave the field of view by the nextframe (due to being pushed out by wind).

If the wind speed and direction are known (for example with an externalwind gauge that communicates with the camera), then we can calculate theprojection onto the image and estimate the amount that the gas will movein terms of pixels in the image. For example, say we find a result thatthe wind motion will cause the gas to move 2 pixels in the horizontaldirection and 0 pixels in the vertical. At block 920, in order toestimate the amount of gas we expect to lose detection to by the time ofthe next frame, we need only sum the total amount of gas that lieswithin the 2-pixel band next to the edge of the image. (This is thehatched region shown in FIG. 10.) For normal situations, the wind speedis such that the number of pixels of motion before the next frame (whenimaging at 15 Hz) is less than 2 pixels, so that interpolation of thepixel values is important.

The method 900 above provides an estimate of the gas emission rate, foreach frame within the video sequence, as shown at block 960. If we sumover all of the images within the sequence then we obtain the total gasemission volume, as shown at block 970, providing the second of thequantities of interest for environmental and leak detection and repair(LDAR) monitoring.

C. Gas Cloud Imager Software Interface

FIG. 11 shows an example of the gas cloud imager (GCI) live viewergraphical user interface. The interface includes a manual record buttontoward the lower right. Recorded videos can be uploaded to a webserverfor easy viewing from a web browser or downloading to a local computer.The interface also includes a countdown bar that informs the operatorwhen the camera is ready to move. To extend time at a particular fieldof view, an operator can click on the “Extend Time” button to the rightof the countdown bar. The system automatically resumes its scan afterthe extended time period is finished. If the operator wants to scanbefore the extend time has finished he/she can click on the resume scanbutton.

FIG. 12 shows an example of the mosaic viewer interface. The GCI'smosaic viewer can be located right next to the live viewer on a separatemonitor and displays the entire monitored area, as shown in FIG. 12.Operators can move the camera to any location in the monitored area bysimply clicking on that portion of the mosaic viewer. The camera willstay at that field until the countdown bar has finished (typically 60secs) and then resumes its automatic motion path. When an alarm hasoccurred in a particular field a red box will highlight in the mosaicviewer until it has returned to that field and not had an alarm event.

FIG. 13 shows an example of the graphical user interface with an alarmcondition. In the event of an alarm, several notifications occur in thesoftware interface as shown in FIG. 13. First, the banner at the top ofthe Live Viewer changes to RED. Second, the detected gas is shown in theGases Detected List. Third, a concentration color bar in ppm-m units isdisplayed to the right of the viewer. And fourth, the gas cloud is falsecolored in terms of its concentration and shown in real time on the liveviewer screen. Behind the scenes, an email is also sent out to all userswith a link to view the gas release from the web server.

FIG. 14 shows an example of an alarm thresholds settings window. At anytime an operator can view the alarm thresholds for each gas beingmonitored by clicking on the settings button in the lower left corner ofthe live viewer, as shown in FIG. 14. To adjust the thresholds anauthorized user can login to the dialog window and adjust the thresholdsfrom the same dialog window.

D. Additional Embodiment of Gas Leak Quantification with a Gas Cloud(Video-Rate Infrared) Imager

The gas cloud imager (GCI) system uses low-resolution spectroscopy toachieve higher SNR than available with high-resolution spectroscopy.While this has the disadvantage of making the system less capable ofdiscriminating among different spectra, it also has the importantadvantage that it is less sensitive to saturation. That is, inhigh-resolution spectroscopy, the sharp absorption/emission features ofgases will tend to saturate (i.e. e^(−α)≠α for absorption coefficient α)even on smaller gas clouds. With low-resolution spectra, however,saturation of these features tends to have little effect on the overallintensity across a measured spectral channel because the sharp featurestend to be too small to dominate the signal. As a result, one can oftenignore saturation effects entirely when working with low-resolutionspectra.

1. Introduction

There is a real need to develop an algorithm oriented towards real-timeautonomous operation. In brief, various spectral infrared gas detectionalgorithms may operate roughly as follows. The algorithm monitors thepixel in the scene and looks for spectral radiance changes. Changes thatcorrespond closely to spectral features of a known gas are classified asa detection, and quantification of the pixel's gas column densityfollows. Summing and scaling all detected pixels within an imageprovides an estimate of the total cloud volume, so that tracking thetotal gas volume over a sequence of frames allows for emissionsmonitoring. Thus, one can think of a certain hierarchy to themeasurement sequence. The primary task is simple detection—the mostimportant thing is to determine whether a gas cloud is present, what gasit is made of, and where it is. The secondary task is concentrationestimation and quantification—we want to know how much gas is presentand what hazards the detected gas poses. The tertiary task is to monitorthe gas overtime and form an emission rate estimate.

In the discussion below, we present the measurement model that thealgorithm is based on and compare it with the similar model typicallyused in the existing literature. After providing practical details forimplementation and quantification, we compare the results of lab andopen-air outdoor experiments to known gas quantities to verify theaccuracy of the method. Finally, we also provide examples of thealgorithm operating on live data streams.

2. Measurement Model

FIG. 15 shows the measurement geometry for a single pixel in a gas cloudimager. The camera line of sight views (1) the background infraredradiation through (2) a gas cloud layer and (3) a foreground atmosphericlayer. The gas cloud measurement model is a two-layer radiative transfersystem (FIG. 15), in which (1) spectral radiance is generated within asource region which can be either an opaque object such as the ground,or the atmosphere itself, such as when viewing the cloudless sky, or acombination of the two. (2) The source spectral radiance next traversesthe gas cloud layer, and is either attenuated or increased by absorptionor emission of gases located there. (3) Finally, the radiation passesthrough a final atmospheric layer before reaching the camera. Thismeasurement model is simpler than the three-layer version often used inthe literature, in which there is an additional background atmosphericlayer between the gas and an opaque radiation source. The simpler modelused here reflects the fact that the autonomous algorithm is agnostic tothe spectrum of the background light—whether the atmospheric layerbehind the gas is absorbing light from an opaque background source or isitself the source of radiation is information that is not used by thealgorithm. Following the literature, we do model both the gas and theforeground layers as being homogeneous (uniform in temperature and gasconcentration).

In the discussion below, we use the following variable definitions

L_(f), L_(g), L_(b): radiances originating from foreground, gas, andbackground layers

M: at-sensor radiance

τ_(f), τ_(g): transmission of foreground and gas layers

T_(f′); T_(g): temperatures of foreground and gas layers

Thus, for a pixel in the scene, using the measurement model shown inFIG. 1, we can write the radiative transfer equation of a ray along theline of sight to given at-sensor radiance M ofM=Lf+τ _(f)ε_(g) B(T _(g))+τ_(f)τ_(g) L _(b),where ε_(g) is the spectral emissivity of the gas. Note that all ofthese quantities have an implicit spectral dependence (i.e. M≡M(λ)etc.). Using Kirchoff's law and an assumption of local thermodynamicequilibrium, we can also make the substitution ε_(g)

1−τ_(g). Since the pixels in the scene can be treated independently, weneed not include the pixel's spatial location within the scene as avariable to model, and thus we can drop the (x, y) dependence from allof the variables and consider only a single pixel at a time.

For passive absorption/emission spectroscopy, the absorption valuesgiven by taking a measurement spectrum and comparing it with a referencespectrum. In the case of gas cloud imaging, we therefore look forspectral radiance changes in the scene that may indicate absorption oremission by a gas cloud by comparing the current frame against areference frame. The reference frame may be a frame obtained at aprevious point in time, or a kind of running average. We write themeasurement at the current frame of the video sequence as M⁽¹⁾ and theradiance measurement of the reference frame as M⁽⁰⁾. Next, if the timedifference between the current frame and the reference frame is short(e.g. not long enough to allow substantial changes in backgroundradiance) then we can take the background and foreground quantities asconstant, while the gas concentration itself varies on shortertimescales:M ⁽⁰⁾ =L _(f)+τ_(f)(1−τ_(g) ⁽⁰⁾)B(T _(g))+τ_(f)τ_(g) ⁽⁰⁾ L _(b),M ⁽¹⁾ =L _(f)+τ_(f)(1−τ_(g) ⁽¹⁾)B(T _(g))+τ_(f)τ_(g) ⁽¹⁾ L _(b).

Empirically, we find that a useful timescale for this is on the order of1 or 2 minutes, beyond which background radiance changes begin to have asignificant influence on the estimated absorption value. Thus, thereference spectral radiance M⁽⁰⁾ is reset approximately every 1˜2minutes to minimize error. (Section 3 below discusses methods forobtaining M⁽⁰⁾.) Taking the difference between the current and referenceframes and simplifying leads toΔM=M ⁽¹⁾ −M ⁽⁰⁾=−τ_(f)(τ_(g) ⁽¹⁾−τ_(g) ⁽⁰⁾)[B(T _(g))−L _(b)],  (1)where we use ΔL, which equals L_(b), for the “radiance contrast” betweenthe gas cloud layer and the background. The sign of the radiancecontrast indicates whether the cloud is observed in emission (ΔL>0) orabsorption (ΔL<0). Next, we can correlate the measured spectral radiancechange at the sensor ΔM(λ) With the known spectral shape of variouslibrary gases, and if the correlation is high enough, and the spectralradiance changes large enough to warrant the change being a result oftrue signal and not noise, then the pixel is labeled as a “detection”and we can continue on to quantify the detected gas. As we will seebelow, a low signal strength can result from either a low gasconcentration or a poor radiance contrast, and in the latter case it isdifficult to obtain an accurate estimate of the concentration, so thatone can either assume a concentration of 0 or use spatial and temporalcorrelations in the data to infer the concentration at a pixel given thevalue at its neighbors. (Note that spatial-temporal correlations amonggas cloud pixels can extend across large regions of the image, and overmany frames of data, so that more than just the nearest neighbors can beused to infer the concentration at an unknown pixel.)

FIG. 16 shows an example absorption spectrum measurement for propylenegas, showing the measured spectrum M(λ). When the background sources ablack-body at T_(b)=0° C., the gas temperature is at T_(g)=30° C., andthe gas column density produces a peak absorption value of A=0.95 (i.e.T=0.05). Note that the measurement spectrum shows a somewhat differentshape than the cross-section spectrum due to the nonlinearity of therelation between absorption and cross-section (α

1−e^(−σnl)).

Once a gas cloud is detected, we can next go on to determine the gasquantity within the pixel. Equation 1 relates the transmission of thegas layer to the measured changes in radiance at the sensor. Using theBeer-Lambert-Bouguer law, the transmission is related to theconcentration and size of the gas as

τ_(g) = exp [−σ(∫₀^(l)n(z)dz)] ≈ exp (−σ nl),where σ is the absorption cross-section, n the gas concentration (numberdensity), and l the path length through the gas. The above approximationbecomes valid when the gas layer is approximately homogeneous. Since themeasurement involves an integral through the gas layer, it is difficultto separate the contribution of the gas concentration n from the cloudpath length l using the radiance value alone, and so we group these twotogether into a single quantity—the column density ζ=nl.

When the gas concentration is low, the transmission can be modeled witha linearized version of the Beer-Lambert-Bouguer equation obtained byTaylor expansion:

$\begin{matrix}{{1 - \tau} = {{1 - e^{- \alpha}} = {{\alpha + {\frac{1}{2!}\alpha^{2}} + \ldots}\; \approx \alpha}}} & (2)\end{matrix}$so that α=−σζ. From (1), the quantity we use during measurement is(τ_(g) ⁽¹⁾−τ_(g) ⁽⁰⁾), which in the thin gas approximation givesτ_(g) ⁽¹⁾−τ_(g) ⁽⁰⁾≈α⁽⁰⁾−α⁽¹⁾=σζ⁽⁰⁾−σζ⁽¹⁾=−σΔζ

The change in gas column density Δζ is the quantity we are looking for.Substituting the above equation into (1), we obtain our estimate of thecolumn density in terms of the measured radiance change and estimatedbackground radiance:

$\begin{matrix}{{\Delta\zeta} = {\frac{{- \Delta}\; M}{\sigma\;{\tau_{f}\left\lbrack {L_{b} - {B\left( T_{g} \right)}} \right\rbrack}}.}} & (3)\end{matrix}$

Finally, we can estimate the background radiance L_(b) by substitutingan hour measurement of the reference radiance value M⁽⁰⁾, so that thefinal equation becomes

$\begin{matrix}{{\Delta\zeta} = {\frac{{- \Delta}\; M}{\sigma\;{\tau_{f}\left\lbrack {M^{(0)} - {B\left( T_{g} \right)}} \right\rbrack}}.}} & (4)\end{matrix}$

All of the variables on the right-hand side of the equation arequantities that we can estimate. The temperature of the gas T_(g) iscommonly assumed to be equal to that of the ambient air, under theassumption that the gas quickly entrains into the local air. For longwave infrared wavelengths (8-12 μm) systems, the important quantitiesthat typically impact τ_(f) for path lengths less than 1 km are those ofwater vapor and dust. Ignoring the presence of spatially-dependent watervapor variation caused by steam, fog, or rain, the overall averageconcentration of water vapor in the ambient air can be estimated with ahumidity sensor, so that together with an estimate of the distance to agas cloud, one can then estimate τ_(f). For shorter measurementdistances, and for those guesses whose absorption features likecompletely outside the water band, τ_(f) can be taken as equal to 1.Finally, the value for a is determined from the type of gas detected,and can be obtained from a spectral library, such as the NIST InfraredDatabase.

An assumption made in going from (3) to (4) is that the referencespectral radiance M⁽⁰⁾(λ) Is an accurate representation of thebackground spectral radiance L_(b)(λ). Section 3 provides details on howthis can be achieved in practice. A second assumption used is that thequantity of interest is the relative change in absorption and not theabsolute absorption value. This makes the system agnostic to thespectral shape of the background source. For continuous monitoringsituations in outdoor environments, this is an important feature, sincemany environmental effects—rain, wind-induced motion of partiallyreflecting surfaces such as tree leaves and man-made signs—createspectral features that can be confused with gas spectral features whenevaluated with low-resolution spectroscopy. And low-resolutionspectroscopy is, in turn, important for providing the camera withmeasurements of sufficient SNR to apply the gas detection algorithms.One can say that this approach prioritizes detection above that ofquantification, so that it allows detection to take place under a wideset of possible conditions, but allows the estimated gas column densityto have more error.

Equation 4 provides the relationships between the change in gas columndensity Δζ, the measured radiance properties, and the known gasabsorption spectrum σ(λ). However, there are two basic methods forimplementing the estimates with an algorithm. The first technique is toaverage the measured absorption ΔM/[M⁽⁰⁾−B(T_(g))] over one or morespectral bands in which the gas absorption cross-section is significant(i.e. not close to zero). If the other quantities on the right-hand sideof (4) are likewise averaged across the same bands, then one obtains anestimate for Δζ with minimal computational effort. A second technique isto use a statistical method to set the gas cross-section spectrum to themeasured absorption spectrum, which is more accurate but involvescareful regularization in the presence of noisy data and (especially)background clutter.

In the presence of multiple gas species, each of which is weaklyabsorbing, the overall absorption can be written as a linear sum overthe component observances of each species. Thus, for N gases, in thethin gas and homogeneous layer approximations

$\begin{matrix}{\tau_{mix} = {{\exp\left\lbrack {- {\sum\limits_{i = 1}^{N}{\sigma_{i}\left( {\int_{0}^{l}{{n_{i}(z)}{dz}}} \right)}}} \right\rbrack} \approx {\sum\limits_{i = 1}^{N}{\sigma_{i}n_{i}{l.}}}}} & (5)\end{matrix}$

If the ratios of the various constituent species within the gas mixtureremain constant, then the gas mixture can be characterized with singleeffective cross-section: τ_(mix)=σ·n·l. Thus, while one may use spectralunmixing and matched filtering algorithms to estimate the columndensities of multiple gases simultaneously, we limit the current exampleto gases in which the mixture ratios are constant, and so can be modeledwith a single effective absorption cross-section.

So far all of the discussion has been in terms of absorption, that ifthe radiance emitted by the gas is brighter than that of the background,then we use emittance c in place of absorption 1−τ, but the equivalencebetween the two under Kirchoff's law means that the only change to theresult is a change in sign. Thus, we can use the same expression foremission as for absorption, where ΔM will be positive in the case ofobserving the gas in absorption, and negative when observing inemission. An important case where observation of gas is commonly seen inemission is that of a sky background. Not only does the sky occupy alarge portion of the field of view in many situations, but it also canhave a large radiance contrast. A clear blue sky background can provideover 100 degrees of thermal contrast for most spectral bands across the8-12 μm spectral range.

3. Estimating the Reference Spectrum of a Scene Pixel

The previous section left out a discussion of how to obtain a good modelfor the reference spectrum of a scene pixel. One simple way of doingthis is to take the reference spectrum as that of a pixel at an initialpoint in time, M⁽⁰⁾(λ)

M(λ,t₀), before the measurements themselves begin. For clarity, we showthe explicit λ-dependence here, and we will also write the referenceat-sensor radiant spectrum as M rather than M⁽⁰⁾ to make explicit thefact that we are using a temporal mean for the reference spectrum. Inorder to improve the SNR of M, one can of course take the mean spectrumfrom the first N+1 frames of data rather than just the frame: M(λ)=

M(λ, t)

_(t=t) ₀ _(, . . . , t) _(N-1) . Taking this another step further, onecan use a continuously updated running mean, and we have foundempirically that this provides good results.

However, while the running average improves detection by improving SNR,problems can occur. Any moving object (such as a car, or a bird) thatenters the scene will likely have a radiance very different from that ofthe background, and so the algorithm might choose between eitherdiscarding the existing reference spectrum for the new, incorporatingthe change into the running mean update, or of maintaining the existingreference and ignoring the update in this case. Since such objects aremoving, they produce rapid radiance changes across those pixels thatthey obscure, and so we find that in practice it is better to maintainthe existing reference without performing an update in this case. Thetrick is to find a criterion by which to discriminate between objectsthat have moved in front of the background, thereby obscuring it—inwhich case an update should not be performed—and a change to thebackground itself—in which case the update should be performed. Anotherproblem that can occur with a running update is that if a gas cloud ispresent in a scene, then its spectral signature can quickly get “burnedinto” the reference spectrum, so that the system loses sensitivity. Wealso want a criterion to minimize this from occurring.

The method we use is an SNR threshold based masking of the updateprocedure. That is, along with the reference spectrum of the pixel, wealso calculate a running estimate of the variance of each spectralchannel of the pixel. Taking the ratio of the running mean with thesquare root of the running variance estimate gives an SNR value at eachspectral channel. The above algorithm therefore becomes, in pseudocode,

while new_data:D=M_i−MbarMbar+=D/iB+=D*(M−Mbar)var_M

V/(i−1)SNR_M=(M_i−Mbar)/sqrt(var_M)where M is written as Mbar, and the at-sensor radiance of the currentframe as M_i, with i the frame counter. The results var_M and SNR_M arethe variance and SNR of the at-sensor radiance. The parameters D and Vare the difference value and statistical second moment, used tocalculate the variance. For the first second of time in which data iscollected, the SNR is calculated over the scene, allowing for all pixelsto be updated. Following that, with each new frame we create a binarymask such that for any pixel spectral channel whose SNR value is above aselected threshold, the running update is not applied. This is thesimple criterion by which the algorithm determines that a new object hasentered the field of view and blocked the background source. For anypixel whose SNR is at or below the threshold, the algorithm applies therunning update to M and var(M).

4. Estimating the Total Gas Quantity

From Section 2, we can determine whether a gas cloud has been detectedin its column density in ppm·m (parts-per-million times meter), orsimilar units. For emissions monitoring and leak rate estimation, wetake a few more steps, the first of which is to convert a gas cloudmeasurement to absolute quantity units. That is, if we know theeffective area of a given pixel, together the column density of gasdetected there, then by multiplying the two we obtain the total volumethat the gas would occupy if it were a constant 1 ppm·m column density.Dividing by 10⁶ gives the effective volume the pure gas would have atstandard atmospheric temperature and pressure. The resulting units canbe given as an equivalent volume of pure gas (e.g. L, m³, or ft³), or,by using the known density of molecules at the gas temperature andpressure, one can estimate the total number of molecules in the cloud.Or, more useful still, one can use the molecular mass of the gas toconvert the number of molecules to a total mass of gas (g, kg, or lbs).

The initial step of this calculation, estimating the projected area of apixel at the cloud, is easily obtained by multiplying the knowndimensions of the detector array pixels (p_(x), p_(y)) by the imagemagnification, which is a function of the focal length f of the cameraobjective lens and the distance z to the gas cloud. FIG. 17 shows adetector pixel projected to the location of the gas cloud. We cancalculate the projected dimension of the pixel P_(x) at the plane of thegas cloud asP _(x) ≈p _(x) z/f.Since most detectors have p_(x)=p_(y), we can write that the projectedarea of the pixel is thereforeA _(proj)(p _(x) z/f)²  (6)

While the pixel dimension p_(x) and f are known as a result of thehardware design, the gas cloud distance z varies and can be estimated.When setting up a gas card imaging camera at a facility, one of theearly set up procedures is to measure the distances from the camera tothe primary items to be monitored. These items are often things such asa collection of tightly interwoven pipes, the wall of a gas containertank, the valves of a gas separator tank, etc. The important thing isthat the general region in which potential leaks may occur is known apriori, and thus the distance to any gas leak can be estimated toreasonable accuracy by using that distance is measured during the systemset up.

While the distance to the gas cloud can be estimated by assuming thatthe gas cloud will occur near the equipment being monitored. There areother techniques which are also available. One can use multiple infraredcameras viewing the same scene to triangulate on the gas cloud. Anothermethod is the use of a laser tracker (or “laser rangefinder”) tuned to awavelength that is absorbed by the gas.

With distance z known, we can apply (6) to scale the measured gas columndensity to units of equivalent volume of pure gas (L, m³, or ft³) simplyby dividing by 10⁶. If the total number of gas molecules is the unitdesired, then one can multiply the equivalent pure gas volume by thenumber of molecules per cubic meter at the ambient atmospherictemperature and pressure. Converting the total number of molecules tothe total gas cloud mass then requires only multiplication by the gas'known molecular weight.

5. Emission Rate Quantification

Once we have an estimate of the total gas volume in a video frame, wecan then start monitoring the gas volume over many frames in an attemptto estimate the rate at which the gas is being emitted from its source.

What is needed is an autonomous algorithm that is amenable to rapidcomputation, and which can estimate this loss of sensitivity to the gasas it entrains into the local air. Our approach is to avoid optical flowcomputations everywhere except the edges of the field of view, andinstead to monitor the measured gas volume together with a heuristicestimate of the sensitivity loss from frame to frame. In the vastmajority of cases—in which the gas leak source is more than a few pixelsaway from the edge of the field of view—the sensitivity loss termdominates over the optical flow term. This means that the optical flowcalculations can be entirely neglected when the amount of gas near theedge of the field of view is small in proportion to the total gasdetected, and this helps to ease the computational burden.

We start by measuring the total amount of gas present in each frame of avideo sequence, and then say that any increase in the total gas measuredindicates the presence of an emission source, with the increase sincethe previous frame giving the leak rate. In an ideal measurementenvironment, this would be all that is needed. The algorithm alsomonitors the edges of the field of view, so that if there is wind in thescene, or if the gas is moving rapidly due to buoyancy effects, then itcan estimate the volume of gas exiting the camera's field of view andadd this amount back into the leak rate. Similarly, if any gas entersthe field of view from outside, then that portion of the gas volume issubtracted from the leak rate estimate. The final step is to develop amethod for measuring sensitivity loss, and augment the leak rateestimate with the corresponding loss term.

Estimating the gas volume decline from frame to frame due to sensitivitylimits is determined using a simple heuristic model, developed asfollows. The algorithm first calculates the range of gas column densityvalues detected within the gas cloud. The threshold is set to be afraction of the range of column density (ppm·m) values above the minimumdetected value. Thus, if the maximum column density value detectedwithin a gas cloud is 5000 ppm·m, and the lowest 100 ppm·m, then thecalculated range is 4900 ppm·m. If we set a threshold as 20% of therange, then the threshold value in units of ppm·m would be(ppm·m threshold)=(minimum ζ)+0.2(ζ range)=100+0.2(4900)=1080.

Next we locate the set of all “edge pixels” in the gas cloud—pixels in acloud that are no more than two pixels away from a pixel where gas isnot detected. We expect that some fraction of edge pixels whose columndensity lies below the calculated threshold will drop below thedetection limit of the camera. Using a series of experimental data, wedetermined empirically that the best value for our camera was 0.25.Thus, the algorithm locates all of the edge pixels that lie below thethreshold, sums up the total gas quantity within them, and multipliesthe result by 0.25. This is the total amount of gas we expect to losesensitivity to by the next frame—the “loss term” that is used to augmentthe leak rate estimate.

The next step attempts to estimate how much gas will exit the edges ofthe field of view between the current and the next frame, or how muchhas entered the field of view from outside it since the previous frame.This either involves knowing the wind speed and direction in terms ofthe GCI's optical axis, or using video analytics to estimate the speedof motion of the gas. If the wind speed and direction are known (forexample with an external wind gauge), then it is a simple calculation todetermine the speed in terms of pixels in the image, and estimate gasmotion in that way. Wind, however, is generally not as well-behaved asthis, so that a unidirectional model of motion will fail to capture theswirls and rapid changes of direction that occur in real life. Thus,estimating flow by modeling the gas motion can be useful for an accuratemeasure Because flow estimation is known to be computationallyintensive, an important means of reducing the size of the problem is torealize that we need only model flow within the outer boundaries of theimage, and not the image as a whole.

Once we add the estimated “sensitivity loss” and “flow loss,” andsubtract the estimated “inward flow” from the current frame's total gasvolume, we can track the changes in this “augmented” estimate of thevolume from frame to frame. The estimated leak emission rate is theamount by which the augmented gas volume has increased since the lastframe. If the augmented gas volume has decreased, then we say that theestimated emission is zero. (That is, the estimate is biased to acceptonly positive values.) Performing this procedure for every frame over anextended period of observation—such as a 10-second period of a videosequence—the algorithm can obtain the average emission rate over thatperiod.

The embodiments described throughout the attached specification,drawings, claims, and appendix have been described at a level of detailto allow one of ordinary skill in the art to make and use the devices,systems, methods, etc. described herein. A wide variety of variation ispossible. Components, elements, and/or steps may be altered, added,removed, or rearranged. For example, method steps shown in the blockdiagrams can be practiced all together or in any sub-combination.Similarly, claim limitations can be separated and/or combined andincluded in any combination or sub-combination.

The devices, systems, and methods described herein can advantageously beimplemented using, for example, computer software, hardware, firmware,or any combination of software, hardware, and firmware. Software modulescan comprise computer executable code for performing the functionsdescribed herein. In some embodiments, computer-executable code isexecuted by one or more general purpose computers (including desktopcomputers, notebook computers, tablet computers, smart phones, etc).However, a skilled artisan will appreciate, in light of this disclosure,that any module that can be implemented using software to be executed ona general purpose computer can also be implemented using a differentcombination of hardware, software, or firmware. For example, such amodule can be implemented completely in hardware using a combination ofintegrated circuits. Alternatively or additionally, such a module can beimplemented completely or partially using specialized computers designedto perform the particular functions described herein rather than bygeneral purpose computers. In addition, where methods are described thatare, or could be, at least in part carried out by computer software, itshould be understood that such methods can be provided on non-transitorycomputer-readable media (e.g., optical disks such as CDs or DVDs, harddisk drives, flash memories, diskettes, or the like) that, when read bya computer or other processing device, cause it to carry out the method.

A skilled artisan will also appreciate, in light of this disclosure,that multiple distributed computing devices can be substituted for anyone computing device illustrated herein. In such distributedembodiments, the functions of the one computing device are distributedsuch that some functions are performed on each of the distributedcomputing devices.

The devices described herein can exchange information with each other,or with other devices, via one or more communication channels. Suchcommunication channels can be wired or wireless, and can includenetworks, such as a Local Area Network, a Wide Area Network, theInternet, etc.

While certain embodiments have been explicitly described, otherembodiments will become apparent to those of ordinary skill in the artbased on this disclosure. Therefore, the scope of the invention isintended to be defined by reference to the claims and not simply withregard to the explicitly described embodiments.

What is claimed is:
 1. An infrared (IR) imaging system for quantifyingone or more parameters of a gas cloud, the imaging system comprising: anoptical system including an optical focal plane array (FPA) unit, theoptical system having components defining at least two optical channelsthereof, said at least two optical channels being spatially andspectrally different from one another, each of the at least two opticalchannels positioned to transfer IR radiation incident on the opticalsystem towards the optical FPA unit; and a data-processing unitcomprising one or more processors, said data-processing unit configuredto acquire spectral optical data from the IR radiation received at theoptical FPA unit, wherein said data-processing unit is configured todetermine absorption spectra data at one or more given pixels of a givenframe by comparing spectral data for said one or more pixels of saidframe with spectral data from one or more prior frames.
 2. A systemaccording to claim 1, wherein said data-processing unit is configured toconsider signal to noise as a criteria for determining whether toinclude data for a particular prior frame in said comparison.
 3. Asystem according to claim 2, wherein said data-processing unit isconfigured to assess signal to noise based on a standard deviation,variance, or a value based on the standard deviation or variance of thespectral data of a plurality of prior frames at said pixel.
 4. A systemaccording to claim 1, wherein said data-processing unit is configured todetermine absorption spectra data at one or more given pixels of a givenframe by comparing spectral data with a statistical value based on datafrom prior frames.
 5. A system according to claim 4, wherein saidstatistical value comprises a running average.
 6. A system according toclaim 4, wherein said data-processing unit is configured to considernoise as a criteria for determining whether to incorporate data for aparticular prior frame into the computation of said statistical value.7. A system according to claim 6, wherein said data-processing unit isconfigured to assess noise based on variation in spectral data of saidprior frames at said pixel.
 8. A system according to claim 1, whereinsaid data-processing unit is configured to determine absorption spectradata at one or more given pixels of a given frame by determining themathematical difference of said spectral data compared to a runningaverage computed from prior frames.
 9. A system according to claim 8,wherein said determining the mathematical difference comprisessubtracting radiance spectral data for a pixel for a current frame and arunning average of the radiance spectrum for that pixel for priorframes.
 10. A system according to claim 1, wherein said spectral datacomprises luminance or radiance data.
 11. A system according to claim 1,wherein said data-processing unit is configured to compare said spectraldata without knowing whether a leak has occurred.
 12. A system accordingto claim 1, wherein the optical system comprises a plurality of IRspectral filters for the different channels.
 13. A system according toclaim 1, wherein the optical system comprises a plurality of imaginglenses for the different channels.
 14. A system according to claim 1,further comprising a display.
 15. A system according to claim 1, whereinsaid data-processing unit is located at least in part remotely from saidoptical system.
 16. A system according to claim 15, wherein saiddata-processing unit is located at least 10-3000 feet from said opticalsystem.
 17. A system according to claim 1, wherein said data processingunit is in operable cooperation with a tangible, non-transitorycomputer-readable storage medium that contains a computer-readableprogram code that, when loaded onto the data processing unit, enablesthe data processing unit to determine absorption spectra data at one ormore given pixels of a given frame by comparing spectral data for saidpixel of said frame with spectral data from prior frames.
 18. The systemaccording to claim 1, wherein the data processing unit is configured toestimate emission rate data for a gas leak using said spectral data. 19.The system according to claim 1, wherein the data processing unit isconfigured to determine an estimate of gas column density at a selectedlocation within the field of view of the optical system.
 20. The systemaccording to claim 19, wherein the data processing unit is configured todetermine the estimate of the gas column density at the selectedlocation within the field of view by averaging over one or more spectralbands a plurality of values from a time series of data that correspondto the selected location.
 21. The system according to claim 19, whereinthe data processing unit is configured to determine the estimate of thegas column density at the selected location within the field of view byfitting a cross-section spectrum of the gas to a plurality of valuesfrom a time series of data that correspond to the selected location. 22.The system according to claim 1, wherein the data processing unit isconfigured to determine an estimate of the total quantity of gas in thegas cloud at a selected location using said spectral data.
 23. Thesystem according to claim 22, wherein the data processing unit isconfigured to determine the estimate of the total quantity of gas at theselected location using knowledge of one or more specifications of theFPA unit, one or more specification of the optical system, distance ofthe optical system to the gas cloud, or combinations thereof.
 24. Thesystem according to claim 22, wherein the data processing unit isconfigured to determine an estimate the total quantity of gas in the gascloud at a plurality of locations within the field of view of theoptical system and sum said estimates to determine an estimate of thetotal quantity of gas within the field of view.
 25. The system accordingto claim 1, wherein the sampling rate of the acquired spectral opticaldata is at least 15 Hz.